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SSE = sum of squared errors | https://openstax.org/books/introductory-statistics-2e/pages/12-formula-review |
n= the number of data points | https://openstax.org/books/introductory-statistics-2e/pages/12-formula-review |
Outlier : an observation that does not fit the rest of the data | https://openstax.org/books/introductory-statistics-2e/pages/12-key-terms |
Analysis of variance extends the comparison of two groups to several, each a level of a categorical variable (factor). Samples from each group are independent, and must be randomly selected from normal populations with equal variances. We test the null hypothesis of equal means of the response in every group versus the... | https://openstax.org/books/introductory-statistics-2e/pages/13-chapter-review |
Each population from which a sample is taken is assumed to be normal. | https://openstax.org/books/introductory-statistics-2e/pages/13-chapter-review |
All samples are randomly selected and independent. | https://openstax.org/books/introductory-statistics-2e/pages/13-chapter-review |
The populations are assumed to have equal standard deviations (or variances). | https://openstax.org/books/introductory-statistics-2e/pages/13-chapter-review |
Analysis of variance compares the means of a response variable for several groups. ANOVA compares the variation within each group to the variation of the mean of each group. The ratio of these two is theFstatistic from anFdistribution with (number of groups â 1) as the numerator degrees of freedom and (number of obse... | https://openstax.org/books/introductory-statistics-2e/pages/13-chapter-review |
The graph of theFdistribution is always positive and skewed right, though the shape can be mounded or exponential depending on the combination of numerator and denominator degrees of freedom. TheFstatistic is the ratio of a measure of the variation in the group means to a similar measure of the variation within the gro... | https://openstax.org/books/introductory-statistics-2e/pages/13-chapter-review |
When the data have unequal group sizes (unbalanced data), then techniques from13.2 The F Distribution and the F-Rationeed to be used for hand calculations. In the case of balanced data (the groups are the same size) however, simplified calculations based on group means and variances may be used. In practice, of course,... | https://openstax.org/books/introductory-statistics-2e/pages/13-chapter-review |
TheFtest for the equality of two variances rests heavily on the assumption of normal distributions. The test is unreliable if this assumption is not met. If both distributions are normal, then the ratio of the two sample variances is distributed as anFstatistic, with numerator and denominator degrees of freedom that ar... | https://openstax.org/books/introductory-statistics-2e/pages/13-chapter-review |
The populations from which the two samples are drawn are normally distributed. | https://openstax.org/books/introductory-statistics-2e/pages/13-chapter-review |
The two populations are independent of each other. | https://openstax.org/books/introductory-statistics-2e/pages/13-chapter-review |
SSbetween=ââ[(sj)2nj]â(ââsj)2nSSbetween=ââ[(sj)2nj]â(ââsj)2n | https://openstax.org/books/introductory-statistics-2e/pages/13-formula-review |
SStotal=ââx2â(ââx)2nSStotal=ââx2â(ââx)2n | https://openstax.org/books/introductory-statistics-2e/pages/13-formula-review |
SSwithin=SStotalâSSbetweenSSwithin=SStotalâSSbetween | https://openstax.org/books/introductory-statistics-2e/pages/13-formula-review |
dfbetween=df(num) =kâ 1 | https://openstax.org/books/introductory-statistics-2e/pages/13-formula-review |
dfwithin=df(denom)=nâk | https://openstax.org/books/introductory-statistics-2e/pages/13-formula-review |
MSbetween=SSbetweendfbetweenSSbetweendfbetween | https://openstax.org/books/introductory-statistics-2e/pages/13-formula-review |
MSwithin=SSwithindfwithinSSwithindfwithin | https://openstax.org/books/introductory-statistics-2e/pages/13-formula-review |
F=MSbetweenMSwithinMSbetweenMSwithin | https://openstax.org/books/introductory-statistics-2e/pages/13-formula-review |
Fratio when the groups are the same size:F=nsx¯2s2poolednsx¯2s2pooled | https://openstax.org/books/introductory-statistics-2e/pages/13-formula-review |
Mean of theFdistribution:µ=df(num)df(denom)â2df(num)df(denom)â2 | https://openstax.org/books/introductory-statistics-2e/pages/13-formula-review |
where: | https://openstax.org/books/introductory-statistics-2e/pages/13-formula-review |
k= the number of groups | https://openstax.org/books/introductory-statistics-2e/pages/13-formula-review |
nj= the size of thejthgroup | https://openstax.org/books/introductory-statistics-2e/pages/13-formula-review |
sj= the sum of the values in thejthgroup | https://openstax.org/books/introductory-statistics-2e/pages/13-formula-review |
n= the total number of all values (observations) combined | https://openstax.org/books/introductory-statistics-2e/pages/13-formula-review |
x= one value (one observation) from the data | https://openstax.org/books/introductory-statistics-2e/pages/13-formula-review |
sx¯2sx¯2= the variance of the sample means | https://openstax.org/books/introductory-statistics-2e/pages/13-formula-review |
s2pooleds2pooled= the mean of the sample variances (pooled variance) | https://openstax.org/books/introductory-statistics-2e/pages/13-formula-review |
Fhas the distributionF~F(n1â 1,n2â 1) | https://openstax.org/books/introductory-statistics-2e/pages/13-formula-review |
F=s12Ï12s22Ï22s12Ï12s22Ï22 | https://openstax.org/books/introductory-statistics-2e/pages/13-formula-review |
IfÏ1=Ï2, thenF=s12s22s12s22 | https://openstax.org/books/introductory-statistics-2e/pages/13-formula-review |
Analysis of Variance : also referred to as ANOVA, is a method of testing whether or not the means of three or more populations are equal. The method is applicable if:all populations of interest are normally distributed.the populations have equal standard deviations.samples (not necessarily of the same size) are randoml... | https://openstax.org/books/introductory-statistics-2e/pages/13-key-terms |
One-Way ANOVA : a method of testing whether or not the means of three or more populations are equal; the method is applicable if:all populations of interest are normally distributed.the populations have equal standard deviations.samples (not necessarily of the same size) are randomly and independently selected from eac... | https://openstax.org/books/introductory-statistics-2e/pages/13-key-terms |
Variance : mean of the squared deviations from the mean; the square of the standard deviation. For a set of data, a deviation can be represented asxâx¯x¯wherexis a value of the data andx¯x¯is the sample mean. The sample variance is equal to the sum of the squares of the deviations divided by the difference of the... | https://openstax.org/books/introductory-statistics-2e/pages/13-key-terms |
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